Nonlinear oscillations of functionally graded microplates

Abstract

The size-dependent nonlinear oscillation characteristics of a functionally graded microplate is investigated numerically, in which all the displacements, i.e. in-plane as well as out-of-plane, and their inertia are accounted for. The potential energy of the functionally graded microsystem is obtained based on a modified version of the couple stress theory, so as to account for size effects, together with the Mori-Tanaka homogenisation mixture model for the graded material property. The kinetic and size-dependent potential energies of the microsystem are dynamically balanced by the work of an external force via the Lagrange equations and truncated employing an assumed-mode discretization scheme. Extensive numerical simulations are conducted upon the discretised model of the microsystem through use of a continuation technique as well as an eigenvalue extraction method (for the nonlinear and linear studies, respectively). The effect of several functionally graded microsystem parameters, namely the material gradient index, the material length-scale parameter, and the frequency and amplitude of an exciting external force on the response is investigated.